Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
760 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#16860795 | C2 | semidirect |
| 2. C2×#22548712 | C2 | semidirect |
| 3. #30632063 | C2 | direct (N × H) |
| 4. C2×C4×C251⋊C8 | C2 | semidirect |
| 5. C2×#127×C251 | C2 | semidirect |
| 9. C2×#16860795 | C22 | semidirect |
| 12. #22548712 | C22 | semidirect |
| 13. C4×C251⋊C8 | C22 | semidirect |
| 17. #127×C251 | C22 | semidirect |
| 26. C2×C251⋊C8 | D4 | semidirect |
| 44. C251⋊C8 | C2×D4 | semidirect |
| 52. C2×C4×C251 | D8 | semidirect |
| 67. C4×C251 | C2×D8 | semidirect |
| 70. C2×C251 | #493 | semidirect |
| 74. C251 | C2×#493 | semidirect |
| 78. C2×#127 | D251 | semidirect |
| 91. #127 | C2×D251 | semidirect |
| 126. C2×C4 | #16860795 | semidirect |
| 142. C4 | C2×#16860795 | semidirect |
| 146. C2 | #30632063 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860795 | 2 |
| C2×#22548712 | 2 |
| #30632063 | 2 |
| C2×C4×C251⋊C8 | 2 |
| C2×#127×C251 | 2 |
| C2×#493 | 251 |